Final answer:
The set of real numbers greater than -4 and up to -1 in interval notation is (-4, -1]. The parentheses signify exclusion of -4 and the bracket includes -1.
Step-by-step explanation:
The set of all real numbers that is greater than -4 and less than or equal to -1, expressed in interval notation, is (-4, -1]. This means that all real numbers that fall within this range are part of the set, including -1 which is the upper bound of the interval. The round parentheses indicate that -4 is not included in the set (it is just greater than -4), and the square bracket means that -1 is included in the set.